Correlators, Feynman diagrams, and quantum no-hair in deSitter spacetime

Abstract

We provide a parametric representation for position-space Feynman integrals of a massive, self-interacting scalar field in deSitter spacetime, for an arbitrary graph. The expression is given as a multiple contour integral over a kernel whose structure is determined by the set of all trees (or forests) within the graph, and it belongs to a class of generalized hypergeometric functions. We argue from this representation that connected deSitter $n$-point vacuum correlation functions have exponential decay for large proper time-separation, and also decay for large spatial separation, to arbitrary orders in perturbation theory. Our results may be viewed as an analog of the so-called cosmic-no-hair theorem in the context of a quantized test scalar field. This work has significant overlap with a paper by Marolf and Morrison, which is being released simultaneously.

57 pages, Latex, several figures. v2: more details given on derivation of parametric formula in sec.5, and exponential decay result in sec. 6, references added, figures added, typos removed

References in corpus (7)

• The IR stability of de Sitter: Loop corrections to scalar propagators
• Resolution of singularities for multi-loop integrals
• IR divergence does not affect the gauge-invariant curvature perturbation
• Constructive ${\varphi }^4$ field theory without tears
• On the FP-ghost propagators for Yang-Mills theories and perturbative quantum gravity in the covariant gauge in de Sitter spacetime
• Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization
• Perturbative Algebraic Quantum Field Theory and the Renormalization Groups

Cited by in corpus (1)

• QFT in the flat chart of de Sitter space